Sub-exponential DDH ⇒ DDH

Fully-black-box reduction · standard model · folklore · security loss: none

Statement

If DDH is sub-exponentially hard for a group generator $\mathsf{GrGen}$, then DDH is hard for $\mathsf{GrGen}$: an efficient adversary has size below $2^{{\lambda }^{\epsilon }}$ for large $\lambda$, so its advantage is at most $2^{-{\lambda }^{\epsilon }}$ — folklore.